Contact problem for a hollow cylinder

Q3 Mathematics

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI:10.1016/j.jappmathmech.2018.03.020

D.A. Pozharskii

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引用次数: 2

Abstract

The axisymmetric contact problem of the interaction of a rigid annular sleeve with an infinite hollow elastic cylinder with an arbitrary wall thickness, which is subjected to the action of a constant internal pressure, is investigated. When the solution of Lame's problem for a hollow cylinder and the integral transformation method are used, the contact problem is reduced to an integral equation with a difference kernel relative to the unknown pressure in the contact area. To solve this equation in the case of relatively wide sleeves, a modification of the singular asymptotic method based on complication of the approximating function for the symbol function of the kernel when the cylinder walls are made thinner is proposed. Calculations are performed for a broad range of variation of the relative thickness of the cylinder walls with approach to values that are characteristic of the theory of cylindrical shells, in which the shell thickness usually amounts to no more than 2% of the radius of the middle surface. ©2017

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空心圆筒的接触问题

研究了在定内压作用下刚性环空套与任意壁厚的无限空心弹性圆柱相互作用的轴对称接触问题。采用积分变换法求解空心圆柱体的拉梅问题时，将接触问题简化为一个与接触区域内未知压力有差核的积分方程。为了在较宽套筒情况下求解该方程，提出了一种奇异渐近法的改进方法，该方法基于圆柱壁变薄时核函数逼近函数的复杂性。对圆柱壁相对厚度的大范围变化进行了计算，接近圆柱壳理论的特征值，其中壳体厚度通常不超过中间表面半径的2%。©2017

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pmm Journal of Applied Mathematics and Mechanics 物理-力学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.